Unsupervised learning of phase transitions: from principal component analysis to variational autoencoders

We employ unsupervised machine learning techniques to learn latent parameters which best describe states of the two-dimensional Ising model and the three-dimensional XY model. These methods range from principal component analysis to artificial neural network based variational autoencoders. The state...

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Bibliographic Details
Published in:arXiv.org
Main Author: Wetzel, Sebastian Johann
Format: Paper
Language:English
Published: Ithaca Cornell University Library, arXiv.org 12.03.2017
Subjects:
Artificial neural networks
Computer simulation
Critical temperature
Ising model
Machine learning
Mathematical models
Monte Carlo simulation
Neural networks
Order parameters
Phase transitions
Principal components analysis
Three dimensional models
Two dimensional models
Unsupervised learning
ISSN:2331-8422
Online Access:Get full text
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Summary:We employ unsupervised machine learning techniques to learn latent parameters which best describe states of the two-dimensional Ising model and the three-dimensional XY model. These methods range from principal component analysis to artificial neural network based variational autoencoders. The states are sampled using a Monte-Carlo simulation above and below the critical temperature. We find that the predicted latent parameters correspond to the known order parameters. The latent representation of the states of the models in question are clustered, which makes it possible to identify phases without prior knowledge of their existence or the underlying Hamiltonian. Furthermore, we find that the reconstruction loss function can be used as a universal identifier for phase transitions.
Bibliography:SourceType-Working Papers-1
ObjectType-Working Paper/Pre-Print-1
content type line 50
ISSN:2331-8422
DOI:10.48550/arxiv.1703.02435